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Re: Still on LOP's (mea culpa)
From: Michael Wescott
Date: 2002 Apr 26, 10:26 -0400
From: Michael Wescott
Date: 2002 Apr 26, 10:26 -0400
>> Given that each observation comes from the same Gaussian distribution >> the joint probability density is proportional to >> >> exp( -(d1**2 + d2**2 + d3**2 ... )) >> >> where dn is the distance from a point to LOP number n. So it's >> a matter of minimizing d1**2 + d2**2 + d3**2 ... to get maximum >> joint prob density or MPP. In other words it's a least squares problem. > Now I am getting confused anew. If the sigma is the same for each LOP, > then how can the expression below weight dN differently from dM. All > the d's are squared inside the exp(). So in a 3-LOP case, how could the > center be anything but the center of the inscribed circle (i.e. all d > the same value)? By geometry. If you move the candidate point for MPP almost parallel to side N and side P, dM can get smaller faster than dN and dP get bigger. It depends on their mutual orientation. -- Mike Wescott Wescott_Mike@EMC.COM